This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A168068 #7 Mar 30 2012 18:52:04 %S A168068 0,0,1,0,1,1,0,1,2,3,0,1,4,3,2,0,1,8,3,4,5,0,1,16,3,8,5,3,0,1,32,3,16, %T A168068 5,6,7,0,1,64,3,32,5,12,7,4,0,1,128,3,64,5,24,7,8,9,0,1,256,3,128,5, %U A168068 48,7,16,9,5,0,1,512,3,256,5,96,7,32,9,10,11,0,1,1024,3,512,5,192,7,64,9,20,11,6,0,1,2048,3,1024,5 %N A168068 Array T(n,k) read by antidiagonals: T(n,2k+1) = 2k+1. T(n,2k) = 2^n*k. %C A168068 The array is constructed multiplying the even-indexed A026741(k) by 2^n, and keeping the odd-indexed A026471(k) as they are. %C A168068 Connections to the hydrogen spectrum: The squares of the second row are T(1,k)^2 = A001477(k)^2 = A000290(k) which are the denominators of the Lyman lines (see A171522). The squares of the row T(2,k) are in A154615, denominators of the Balmer series. Row T(3,k) is related to A106833 and A061038. %e A168068 The array starts in row n=0 with columns k>=0 as: %e A168068 0,1,1,3,2,5,3,7,4, A026741 %e A168068 0,1,2,3,4,5,6,7,8, A001477 %e A168068 0,1,4,3,8,5,12,7,16, A022998 %e A168068 0,1,8,3,16,5,24,7,32, A144433 %e A168068 0,1,16,3,32,5,48,7,64, %e A168068 0,1,32,3,64,5,96,7,128, %p A168068 A168068 := proc(n,k) if type(k,'odd') then k; else 2^(n-1)*k ; end if; end proc: # R. J. Mathar, Jan 22 2011 %K A168068 nonn,easy,tabl %O A168068 0,9 %A A168068 _Paul Curtz_, Nov 18 2009